Just intonation whistles - how?

[hans]

I do find the charts a bit strange Hans. I operate in JI. To me ET and the mean tone temperements should be related to JI and not the other way round.

Using the logarithmic cent scale is purely for conveniance. It gives me a chance to check tunings with a digital tuner, which is based on ET. But the whole cent numbers I gave are only approximate, and the ratios are the real thing. To tune by ratio means tuning by ear, using a drone note. That is more accurate than using a digital tuner and aiming for cent deviations.

But I disagree that ET should be related to JI. ET is its own system. It is logarithmic with a firm mathematical and physical foundation. And it is widespread, and used by all common digital tuners. To say that for instance a ET major fourth is so-and-so-much of a ratio bigger than a JI major fourth would not be very helpful, but to say that the JI major fourth is approx. 14 cents lower than the ET major fourth is. Just a matter of practicality.

And if you combine in the theory various intervals, stack them up, so to speak, you'd need to multiply or divide ratios. Or you could add or subtract cent values. Makes the math sometimes easier, even though we just use rounded cent values. But the precision lies in using ratios only. In theory, and in your ears.

[david_h]

Can think of the scale in cents as being being like a tape measure, but better because 1200 increments has a non-arbitrary meaning

[highland-piper]

As a backer, I dont tune to ET. I use a sweetened temperment,( using my tuner)

Peterson tuner? Which sweetening work best? I haven't actually tried that function yet. But I did set it up for bagpipe chanter, and it's pretty nifty, but not as good as I was expecting. I'm wanting to try it out for making whistles, but I haven't gotten around to making any whistles since I got the tuner.

[highwood]

Boy - don't sign in for a couple days and four pages ...

where to start, well I've come in late so I'll just make a comment on

But your classical violinist only has one C# for playing a solo melody line

that I can't let go - this just seems wrong, I did check out the web site mentioned but did not explore it to find out what it said - I will look in to this further.

and (hopefully helping the original question) ...

a d whistle only plays in a few keys, most commonly D and G and the various related modes. So the whistle only needs to play in a few keys.
I make whistles and have spent considerable time figuring this out with math and playing, and math and playing and... This is how I do it:
If you tune the whistle for a JI D it also works for a JI G - this would be a perfect fifth and forths for the D, G and A and then the 'flat thirds' for F# and B, this leaves the E, C# and Cnat to figure out. I use a flat third from A for the C# (this helps with the cross fingered Cnat) and don't worry to much about the Cnat as I half hole it (a whole other discussion) That leaves the E. Since I like and play tunes in E dorian I need the low E to work with the 'flat' B
So I tune the E flat - I also find that it is much easier to blow a note up in pitch than to get it to sound good lower than it wants to play.

This does have repercussions - before Christmas I was working on playing Carols in some odd keys for a whistle and was working out which whistle to use - though it would seem to make sense to use say an A whistle and a couple of half hole or cross fingerings it did not work I believe because the tuning was now just plain wrong for key. I know an example would be good, I'll try to remember. So maybe I need a ET tube for these keys or a Ab whistle (or whatever)

[Mitch]

WOW!

It's heartenning to see how this topic gets more and more strong answers each time it gets raised!

There seems to be an exponential rise in the interest we show in harmony (Temperament). The art is being advanced!!

As I understand it, any kind of accurate-tuned scale is a new thing to many instruments .. Uilleann pipes being a case in point - they have only had regard for JI or EI in the last 30 years.

Seems that the players found music in them within the frame of the instrument well before anything got codified. If one were to analyse what they did, one could probably find an established intonation schema to fit .. the players themselves did not need to know - they already had ears.

I am glad that whistles can be blown sharp or flat - one must listen to what one is playing .. and what the others are playing.

Most of all, a player must play .. I'm sure 3 bricks of random size and a lump of iron could produce a dance in the heart of someone who cared to do so.

Continue with the math - a lot of music dwells in symbol-space

(Edited to say: Continuity is safe .. we obsess on it .. without it, there would be no miracles when it fails .. we all love the miraculous, but god never cared. Music is close to god .. safety is delicious, but with a dash of goat!!?? mmmmmmm - That's music!).

[hans]

Try this software tuner:
22 Sruti Keyboard And Just Intonation Tuner
Download from http://www.mediafire.com/?ljr44lwzoyj for Windows, freeware with no junkware.

This is a software 22 Sruti keyboard, which has decent sound samples, for different instruments, plus a tampura drone. It uses the south Indian Carnatic Sruti intonation system, which uses 22 just intoned notes to the octave, having two variations for each of the (Western) twelve semitones, except the root note and the Fifth, which have no variations. This is used to precisely tune an instrument for playing a particular raga, with its particular just intonation intervals, usually as seven notes in the octave.

The note names on the keyboard are derived from Indian Sa-Re-Ga-Ma notation, so here is a table with the names of a C and a D scale, and the respective ratios and cent values from the root note.

Code: Select all

D scale D    Eb-      Eb+    E-    E+   F-     F+   F#-  F#+    G    G+
C scale C    Db-      Db+    D-    D+   Eb-    Eb+  E-   E+     F    F+
Sa-Re-  Sa   Re1      Re2    Re3   Re4  Ga1    Ga2  Ga3  Ga4    Ma1  Ma2
Ratio   1:1  256:243  16:15  10:9  9:8  32:27  6:5  5:4  81:64  4:3  27:20 
~Cents  0    90       112    182   204  294    316  386  408    498  520

D scale G#-    G#+    A    Bb-     Bb+  B-   B+     C-    C+   C#-   C#+      D
C scale F#-    F#+    G    Ab-     Ab+  A-   A+     Bb-   Bb+  B-    B+       C 
Sa-Re-  Ma3    Ma4    Pa   Da1     Da2  Da3  Da4    Ni1   Ni2  Ni3   Ni4      Sa
Ratio   45:32  64:45  3:2  128:81  8:5  5:3  27:16  16:9  9:5  15:8  243:128  2:1
~Cents  590    610    702  792     814  884  906    996   1018 1088  1110     1200

I took the liberty adding - and + to the Western note names, to indicate their relative flatness and sharpness (relative to ET).

I recommend you fire up the software keyboard, then select a D tampura, and select a D keyboard, in their drop-down boxes. There is a flute under instruments, and also a guitar, which has some good sustain. Then just explore the keyboard, playing various just intoned intervals, and then modal scales.

Modal JI scales:

Code: Select all

Ionian:
C    D+    E-    F     G    A+     B-    C
Sa   Re4   Ga3   Ma1   Pa   Dha4   Ni3   Sa

Mixolydian:
C    D+    E-    F     G    A-     Bb-   C
Sa   Re4   Ga3   Ma1   Pa   Dha3   Ni1   Sa

Dorian: 
C    D-    Eb-   F     G    A-     Bb-   C
Sa   Re3   Ga1   Ma1   Pa   Dha3   Ni1   Sa

Aeolian:
C    D-    Eb-   F     G    Ab+    Bb+   C
Sa   Re3   Ga1   Ma1   Pa   Dha2   Ni2   Sa 

Phrygian:
C    Db+   Eb+   F     G    Ab+    Bb+   C
Sa   Re2   Ga2   Ma1   Pa   Dha2   Ni2   Sa 

I hope you don't call me totally bonkers, but all the important just interval ratios are on this keyboard, and it it easy to compare various scale patterns, the differences of flattened and sharpened intervals etc.
It is certainly an unfamiliar keyboard layout, but keep in mind that for a seven tone scale you pick just one of the four variations per note name.

Just noticed that the "flute" voice has not all the upper notes, the "guitar" is fine though. And to start the tampura drone you need to click on the image button.

[talasiga]

BTW folks can you now see why what we consider as "modes" of a scale are actually scales in their own right?

JI Aeolian cannot be had as a relative of a JI Ionian (as is faked in ET).
You don't automatically get a B Aeolian that sounds good to the ear using the notes of D Ionian.

Yes, good points! And the rest of your post, concerning solo playing!

It encourages me to think that the Indian JI major tuning is really the best basis for a just intoned whistle or flute. It leaves the problem with the fifth for B Aeolian on a D whistle, but it gives a good Dorian instead, which is more important. And let's play in B Aeolian on an A whistle!

Yes, thanks.

However just some point of difference.The so called "wolf whistle" is not universally found untasteful, not even among Western composers. I posted a link sometime ago to an American composer who talked on this.

The other thing is I query your info on the so called JI Indian major.
In the deepest classical, different raags will have different intonations albeit they (notionally) belong to the same scale,.
For instance, when we practice dhrupad (the preemeninent microtonal and oldest extant genre), we distinguish strongly between the minor 3rd (komal Ga) of these 2 Aeolian raags:
Jaunpuri and Darbari Kanhra

The former, a morning raaga, needs a minor 3rd a tad sharper than the latter, a late night raaga.
While all raags with a perfect 5th will have the JI perfect fifth two cents above ET, the other intervals will vary.

My guess is that wherever you got your info. its from someone who has ARBITRARILY decided to pick one of umpteen major scale raagas for his example. It is dangerous to make a genralisation like this if that is what has happened.

[hans]

Thanks, I happily stand corrected. It is difficult to find names, let alone right names, to JI scale patterns. I am not sure where I picked up the term "the Indian JI major scale", but I pointed out later that on this wikipedia page about JI two Indian JI major scales are mentioned, as well as the Carnatic 22 Sruti intonation system:
http://en.wikipedia.org/wiki/Just_intonation

The section about Indian scales mentions the use of both 5:3 and 27:16 for the Sixth, depending what fits better. I only mentioned 27:16, so I stand corrected. It does outline the issue of wolf intervals, but says that in the melodic context of Indian music, with just the use of drones, it is not a problem. Same goes for the Irish and Scottish music tradition, which is not polyphonic.

If you have a name for the particular major JI scale which uses 27:16 for the Sixth I would be happy to hear it.

I did not say wolf intervals are untasteful. But they may well be undesired. This would be the case playing E Dorian on a D JI whistle, which has the B tuned 5/3 to the root D, or playing B Aeolian on a D JI whistle, which has the B tuned 27/16 to root D.

[talasiga]

appreciate your response.
no I am not up to scratch on the precise maths of the intonations
without reference.
And all that formulaic stuff, simple as it probably is, is not within my working grasp.

My experience is, instead, of the actual differences in the sounds that I have heard in demonstration and strived for in practice.

[walrii]

@walrii: ...the cent deviations look wrong to me.

Now lets construct Dorian on the second note (E on a D major scale):
If we use ratios we divide all ratios by 9/8.

Good eye, Hans. The G maj scale uses the formula you outline here and (I think) is correct. The other modes have an error in the formula that got propagated through the spreadsheet thanks to the magic of digital manipulation. Thanks for catching the error. Now, somehow, the board won't let me back in to edit the thing!

So there is no just intonation scheme which will get all intervals in all main modes right.

Precisely.

[hans]

As talasiga pointed out: what we call modes are scales in their own right, and cannot for JI be derived simply by shifting the starting point, as can be done with ET:
Ionian: (221)2(221)
Dorian: (212)2(212)
Phrygian: (122)2(122)
Mixolydian: (221)2(212)
Aeolian: (212)2(122)
1= ET semi tone
2= ET whole tone
In brackets: lower and upper tetrachords

But we can describe JI modal scales with similar looking JI intervals:
T = 9:8 major tone, ~204 cents
t = 10:9 minor tone, ~182 cents
s = 16:15 semi tone, ~112 cents
Ionian: (Tts)T(Tts)
Dorian: (tsT)T(tsT)
Phrygian: (sTt)T(sTt)
Mixolydian: (Tts)T(tsT)
Aeolian: (tsT)T(sTt)

In the modal scales above all tetrachords form a pure Fourth,
and each scale has a pure Fifth thanks to the major tone T at the centre (pure fourth plus major tone = pure fifth).

I took care to use only the following tetrachord patterns:
Tts for a major tetrachord
tsT for a minor tetrachord
sTt for a phrygian tetrachord
This gives good sounding modal scales.

But it also makes it clear that only some patterns can be derived by shifting the stating point:
The Dorian pattern is the same than the Ionian starting on the second.
The Mixolydian pattern is the same than the Ionian starting on the fifth.
But we don't get the Phrygian nor the Aeolian by starting on the third or sixth of the Ionian, instead we get a minor tone t at the centre, which means the fifth is not pure.

The conclusions are exactly the same:
For a JI whistle design we need to introduce some compromise somewhere, or optimise the design to play for certain modes, and other modes need intonation shifts by the player. And there is no one answer.
On a D whistle the notes which needs varying are mainly E and B, depending on which JI scheme the design is based on.

[david_h]

But we can describe JI modal scales with similar looking JI intervals:
T = 9:8 major tone, ~204 cents
t = 10:9 minor tone, ~182 cents
s = 16:15 semi tone, ~112 cents
Ionian: (Tts)T(Tts)
Dorian: (tsT)T(tsT)
Phrygian: (sTt)T(sTt)
Mixolydian: (Tts)T(tsT)
Aeolian: (tsT)T(sTt)
<snip>... it also makes it clear that only some patterns can be derived by shifting the stating point...

That's a neat way of showing it.

It also makes clear that if on our (Tts)T(Tts) D whistle we want to play in G then we end up with a G scale that starts with a (TTs). So if we have a Christmas carol that would fit on the whistle in D but play it in G to keep the singers happy it sounds different. And those Merry Gentlemen will rest differently in Bm than they do in Em.

But if we changed the B to make other modes worked better we could then get G scale that ... oh never mind, this could go on for ever.

[hans]

If we optimise the D whistle design for G major we get these patterns from the whistle root:
TtsTtsT (using Cnat)
TtsTtTs (using C#)
or D E+ F#- G A B- C-/C#- D
+ and - as indicators for sharpness / flatness (though we have precise values for this).

With such a whistle we can play naturally in G major, D mix, A dor and F# phrygian. And by blowing the B sharp we can play in D major, E dor, A mix and E nat minor (Aeolian).

Tuning differences from ET are:
D:0 E:+4 F#:-14 G:-2 A:+2 B:-16 Cnat:-4 C#:-12 in cents
The B needs to be blown sharp 22 cents to +6 ET for Dmaj, Edor, Emin, Amix.
Perhaps it is wiser to tune it slightly less flat, and adjust downwards and upwards as needed?

[david_h]

If we optimise the D whistle design for G major we get these patterns from the whistle root:
TtsTtsT (using Cnat)
TtsTtTs (using C#)

Thats where we were in the table at the end of the previous thread (hows the horse ? Still breathing ?) I rambled on to suggest a G# of 45/32 from D that gave an A major scale that went (tTs)T(tTs). Different sounding again. It explains why, as highwood was saying higher up, getting a tune to sound the same in different keys is not just a matter of pitching the cross-fingered or half-holed note as required.

A have to admit that from a personal perspective I have only recently got my ear and playing to the point where this is significant. But it helps to have the explanation that some of the challenge is inherent in the instrument.

The solution seems to be to buy lots of whistles. Or a flute.

[hans]

The B is easy to blow sharper, and only gets a few decibel louder. Nothing compared to an octave jump, which doubles the loudness on the whistle. So I am happy to live with some compromise.

As for the horse still breathing: I don't mind going in circles sometimes. I certainly got a better understanding now. And this just intonation tuner software I mentioned. Both will help me train my tuning ear, and will result in more accurate tuned whistles.